Handling equivalence classes of Optimality-Theoretic comparative tableaux

• Autorzy: Yanovich I.

Identyfikatory

DOI

10.15398/jlm.v2i2.77

• Języki publikacji: EN

Abstrakty

EN

Many Optimality-Theoretic tableaux contain exactly the same information, and equivalence-preserving operations on them have been an object of study for some two decades. This paper shows that several of the operations proposed in the earlier literature together are actually enough to express any possible equivalence-preserving transformation. Moreover, every equivalence class of comparative tableaux (equivalently, of sets of Elementary Ranking Conditions, or ERC sets) has a unique and computable normal form that can be derived using those elementary operations in polynomial time. Any equivalence-preserving operation on comparative tableaux (ERC sets) is thus computable, and normal form tableaux may therefore represent their equivalence classes without loss of generality. Optimality Theory (OT) is a grammatical formalism based on constraint competition, formulated by Prince and Smolensky (1993) (later published as Prince and Smolensky (2004)). OT is especially popular in phonology, and is used to some extent in other branches of linguistics. In OT, a set of competing output forms {Output₁, Output₂,…} is generated by machine Gen for the underlying form Input. Each pair <Input, Output_N is then evaluated against a set of constraints Con. The grammar of a particular language is modeled as an ordering of the universal set of constraints Con which determines the winning input-output pair for each Input: an input-output pair α = <Input, Output_N wins over another pair β = <Input, Output_M when α incurs fewer violations than β in the most highly ranked constraint where α and β differ. The input-output pairs that do not lose to any other pair are declared grammatical. The OT formalism expresses two important intuitions regarding how languages might function. First, it easily captures conditions of the form “try A; if impossible, try B; if also impossible, resort to C”, which seem to frequently occur in natural language. Second, OT allows for elegant modeling of cross-linguistic variation and language change in terms of re-ranking of a universal set of constraints. The information that a given dataset contributes constrains the possible rankings of constraints. Such information may be represented in the form of a comparative tableau (Prince 2000) or the corresponding set of Elementary Ranking Conditions, or ERC set (Prince 2002). In this paper, I present an incremental step completing the development of a full theory of equivalence classes of comparative OT tableaux, or, equivalently, ERC sets. Earlier work, especially that of Hayes (1997), Prince (2000), Prince (2002), Brasoveanu and Prince (2011)¹, and Prince (2006), has established a number of results concerning how one may transform the information in an OT tableau without loss. What has not yet been done in this line of research is to establish the limits of operations that preserve equivalence. For example, the following natural question has not been answered: given two arbitrary comparative tableaux or ERC sets, can we determine whether they contain identical information?² The present paper fills this gap: I show that any (finite) comparative tableau may be (computably, and actually quite efficiently) transformed into a normal form, which is unique for the whole equivalence class. Moreover, this transformation is possible by applying a sequence of a set of five elementary operations and their inverses already introduced in the literature. Only two of those are non-trivial, so a very small and simple set turns out to be sufficient to capture all the diversity of possible equivalence-preserving operations on tableaux. Normalization gives us a handle on equivalence classes of tableaux/ERC sets, as we show that each equivalence class contains exactly one normal form tableau. The normal form may therefore serve as the class’s representative. A test for equivalence of arbitrary tableaux (computable for finite tableaux) involves normalizing the input tableaux and comparing the resulting normal form tableaux. The original tableaux are equivalent if and only if their normal forms are identical. Thanks to the normal form theorem proved in the present paper, the space of all possible equivalence-preserving operations may be enumerated, and the same is true of the members of which equivalence class.

Słowa kluczowe

EN

Optimality Theory; ERC set; tableau equivalence; normal form; equivalence-preserving transformations

• Wydawca: Instytut Podstaw Informatyki PAN
• Czasopismo: Journal of Language Modelling
• Rocznik: 2014
• Tom: Vol. 2, No. 2
• Strony: 285--306
• Opis fizyczny: Bibliogr. 11 poz., tab.

Twórcy

autor

Yanovich I.

• Tübingen University, Germany

Bibliografia

• [1] Adrian Brasoveanu and Alan Prince (2005), Ranking and Necessity, Part I, Rutgers Optimality Archive 794.
• [2] Adrian Brasoveanu and Alan Prince (2011), Ranking and Necessity: the Fusional Reduction Algorithm, Natural Language and Linguistic Theory, 29 (1): 3-70, revised version of Brasoveanu and Prince (2005).
• [3] Bruce Hayes (1997), Four Rules of Inference for Ranking Argumentation, ms., UCLA. http://www.linguistics.ucla.edu/people/hayes/otsoft/argument.pdf.
• [4] Renè Kager (1999), Optimality Theory, Cambridge University Press, Cambridge.
• [5] Giorgio Magri (2009), A Theory of Individual-Level Predicates Based on Blind Mandatory Implicatures. Constraint Promotion for Optimality Theory, Ph.D. thesis, MIT. http://dspace.mit.edu/handle/1721.1/55182.
• [6] Alan Prince (2000), Comparative tableaux, Rutgers Optimality Archive 376.
• [7] Alan Prince (2002), Entailed Ranking Arguments, Rutgers Optimality Archive 500. http://roa.rutgers.edu/article/view/510.
• [8] Alan Prince (2006), No more than Necessary: beyond the Four Rules, and a bug report, Rutgers Optimality Archive 882. http://roa.rutgers.edu/article/view/905.
• [9] Alan Prince and Paul Smolensky (1993), Optimality Theory: Constraint Interaction in Generative Grammar, Rutgers Optimality Archive 537. http://roa.rutgers.edu/article/view/547.
• [10] Alan Prince and Paul Smolensky (2004), Optimality Theory: Constraint Interaction in Generative Grammar, Blackwell, Oxford.
• [11] Igor Yanovich (2011), On sets of OT rankings, Rutgers Optimality Archive 1149. http://roa.rutgers.edu/article/view/1203.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).